Doppler is a familiar phenomenon in which the frequency of a received signal appears to change as the radial velocity between the transmitter and receiver changes. Historically, this change in frequency has been modeled as a translation in frequency, but, as we will show, this model is not correct. The correct model is that Doppler results in a change of scale of the time axis of the signal.
Perhaps the first application of the Doppler equation was the measurement of the velocity at which stars are moving away from us. Under the big bang theory, this information can be used to estimate the distance of stars in the universe. In estimating the velocity of stars, light from an individual star was isolated and passed through a prism. The emission spectrum of an element, such as hydrogen, was identified and the apparent shift of one spectral emission component was measured to determine the star's velocity. In this case, the Doppler shift is easily measured since emission spectra consist of the sum of isolated sine waves at precise known frequencies.
A quarter century ago, in “Algorithms for Ambiguity Function Processing” by S. Stein, IEEE Trans. Acoust., Speech and Signal Processing, vol. ASSP-29, Stein proposed a method for geolocating emitters from the signals collected by two receivers. In Stein's formulation of the problem, either the transmitter or the receivers are assumed to be moving, and the position and vector velocities of the receivers are assumed to be known. Stein assumed the CAF model in which Doppler is modeled as a translation as a translation in frequency. This application of the CAF was quite clever since knowledge of the time delay and frequency delay between the two received signals resulted in two potentially independent curves representing two possible emitter locations of constant time delay and constant frequency delay, respectively. This is the process currently used in nearly every geolocation application involving two or more receivers. It has been applied to a variety of problems, such as GPS and bistatic radars, in which the reflection from the target are received and processed by two or more radar receivers. Although the Stein formulation accurately represents signals at narrow bandwidth, it models the signal as a sine wave. This is an incorrect assumption for broad bandwidth signals, and therefore, the Stein formulation has significant disadvantages that must be addressed. Despite these drawbacks, many prior art methods continue to rely on the Stein formulation.
U.S. Pat. No. 6,636,174, entitled “SYSTEM AND METHOD FOR DETECTION AND TRACKING OF TARGETS,” discloses a method of using a fractional Fourier transform in a CAF to track objects. This method is useful, for example, in radar and sonar systems to find position and estimate the velocity of signals. By altering computations in this method, the signals can be mapped to polar coordinates, as opposed to Cartesian, which is more accurate for certain types of signals. However, it does not address the problems solved by the present invention. U.S. Pat. No. 6,636,174 is hereby incorporated by reference into the present invention.
U.S. patent application Ser. No. 10/996,462, entitled “QUANTUM CROSS-AMBIGUITY FUNCTION GENERATOR,” discloses a method of applying quantum mechanics to the traditional cross-ambiguity function to achieve more accurate computations at increased bandwidths for both geo-location and radar applications. The constructed cross-ambiguity function generator, rather than having either an analog or digital construction, has a construction based on the properties of quantum physics based on electro-optical elements. Because the invention is based on different technology than existing systems, the advantages obtained by this invention will require significant investment by current users to implement. Further, it does not solve the problem addressed by the present invention. U.S. patent application Ser. No. 10/996,462 is hereby incorporated by reference into the specification of the present invention.
U.S. patent application Ser. No. 11/180,811, entitled “METHODS FOR DETECTION AND TRACKING OF TARGETS,” discloses a method of detecting and tracking targets. Specifically, signals are received and reflected from targets and processed to compute slices of the CAF. These slices are used to find the signal delay and Doppler shift associated with the targets, which facilitates tracking and targeting. This method attempts to solve the problem by only calculating slices of the CAF, thus simplifying computation. This does not result in the improvement in accuracy achieved by the present invention. U.S. patent application Ser. No. 11/180,811 is hereby incorporated by reference into the present invention.
Although prior art methods have been developed for locating and tracking a receiver, specifically in satellite applications, these methods are primarily accurate only in narrowband applications. Methods that have attempted to account for problems beyond the narrow bandwidth case require extensive modifications to existing equipment, and therefore are impractical for users or manufacturers to implement from both a cost and efficiency standpoint. What is required in the art is a method of processing signals to determine position and velocity of a transmitter accurately over a wide range. of bandwidths.